60 points by deepimagedata 1 year ago flag hide 24 comments
curiousai 1 year ago next
Fascinating article! I never thought about applying closed-form solutions to image segmentation. I wonder how the performance compares to deep learning for this task?
neuralnick 1 year ago next
Closed-form approaches are mathematically elegant and usually faster, but they can lack flexibility compared to deep learning models.
ml-miracle 1 year ago prev next
An interesting comparison of both techniques on a standard image segmentation dataset would make an excellent follow-up article!
tensorlady 1 year ago prev next
So, what kind of constraints does one impose to derive closed-form solutions for image segmentation? It feels pretty magical...
puremathjim 1 year ago next
It's actually based on energy minimization principles and required assumptions on the image data. This MIT video lecture series explains it well: https://www.youtube.com/watch?v=J-KIKBmWqxo&ab_channel=MIT
visionveteran 1 year ago prev next
I have always used statistical model-based methods or deep learning models for image segmentation. Thanks for enlightening me on this alternative method.
infocrunch 1 year ago next
These closed-form solutions arise from the field of convex optimization and provide quick, analytical solutions. Def worth a read!
curiousai 1 year ago prev next
Thanks, @neuralNick. I think there is still much to discover about this elegant method. I'll check out that video lecture series, @pureMathJim.
tensorlady 1 year ago next
@curiousAI, me too! I'm looking forward to that follow-up article and I want to learn more as well.
handee 1 year ago prev next
One challenge I see is noise in real-world images. Any thoughts on how closed-form solutions tackle image imperfections?
turingtest 1 year ago next
That's a fair concern, @hanDee. Appropriate regularization and priors could help address image imperfections. But yeah, a detailed analysis would help.
qnguyen 1 year ago prev next
The idea of extending closed-form solutions to video segmentation is enticing. I wonder what the challenges would be in that domain.
ml-miracle 1 year ago next
I agree, @QNguyen. Incorporating temporal coherence and motion estimation in closed-form solutions could be fascinating research.
optirob 1 year ago prev next
I'm new to HN and image processing. I recently took a course on convex optimization. Could this bridge the gap and answer my questions about image segmentation?
matrixmike 1 year ago next
Absolutely, @optiRob. Implementing closed-form solutions can be an ideal way to apply your theoretical understanding of convex optimization practically.
aiartist 1 year ago prev next
@optiRob, check out Boykov and Veksler's work on graph cuts for a simple entry point. That surely ties your knowledge of convex optimization to image segmentation.
mathmagician 1 year ago prev next
Closed-form solutions are often based on assumptions and constraints. How well do these solutions generalize to different types of images?
neuralnick 1 year ago next
Generalization depends on the assumptions made and data used to derive the closed-form solutions. A closer look at those factors will cover this question's depth.
markovmark 1 year ago prev next
I'd like to learn more about the actual code implementing this technique. Open-sourcing the project will help others build on it.
bildpilotin 1 year ago next
Totally agree, @markovMark. Sharing code is a great way to foster community learning and spark incremental improvements. Maybe it will be available soon.
mathwizardess 1 year ago prev next
Is there a succinct mathematical explanation of closed-form image segmentation solutions in the article? I'd love a summary of the technique!
secant27 1 year ago next
Not in-depth, but the basics are covered. You might want to read those classic papers on Graph Cuts for a deeper dive - particularly this one: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.6166
robopsycho 1 year ago prev next
Can closed-form solutions be compared to watershed segmentation techniques? If so, where does one start?
pixelpuzzle 1 year ago next
@robopsycho, a comparison can be drawn by considering both as energy minimization techniques. Arulampalam et al. did a nice job in explaining watershed in the context of energy minimization. http://users.cecs.anu.edu.au/~Steve.Blackburn/pubs/niepce_energysurfaces.pdf